In this paper, following [1]}, we use a simple and general definition of weak coreset, that is also more practical. Instead of defining a unique (static, global) set \(Q\)  of queries, we define \(Q\)  to be a function that maps every subset (potential coreset) \(S\)  of \(P\)  to a set of queries. A weak coreset \(S\)  needs only to approximate the queries in \(Q(S)\) . It turns out that for many case the (generalized definition) of dimension for such a query space is much smaller compared to the traditional case where \(Q(S)=Q(P)\)  is the same for every subset \(S\subseteq P\) .
